You probably want a good chimney sweep as a start. In my limited experience, they're very good at assessing chimney condition, and they're usually pretty "frank."
Also, don't expect a smoke pellet to work if: the air on the roof is significantly warmer than the air in the room, or there's no way for air to enter the room at low level either.
Chimneys aren't magic - air is heated and rises, sucking more with it as it goes. If it can't flow properly it can't rise. That's how you get CO2 and CO buildup - in the first case combustion happens properly but the exhaust gases can't rise fast enough. In the second case airflow is so poor that the build-up of CO2 impedes combustion too so that it's incomplete (and you get CO instead of CO2). Both are poisons, but CO is really dangerous as it's more chemically active in the body.
Check there's a permanent route for quite a large volume of air to reach the fireplace.
If you need to do a test before any necessary vents are done (modern windows stop the draughts that used to help in the C19th!), do the test with the room door open, on a cooler day.
Most brick chimneys are 1/2-brick where they go through the attic and the chimney breast brickwork, and between houses in back-to-back chimneys (often a cause of noise complaints - effectively the two properties are connected through missing pointing in the chimneys). The only practical solution if you can't repoint them effectively is a liner. Bear in mind that, if back-to-back, you may fix your problem with repointing but create one for the other party (and some danger too, as both CO and CO2 are heavier than air so sink through the house as they cool.
I am NOT a builder, nor a heating specialist. You should get proper advice. I've only posted the above to give you some idea of the issues. FIrst off, you probably need it cleaned anyway, so find a sweep and make the chap a big mug of tea...
 got CO and CO2 the wrong way round - CO comes from poor combustion, CO2 when things burn properly.[/]
Chimney inspected today by the cleanest looking chimney sweep !! I was actually surprised at how clean he looked
Anyway, all good news, he says the liner is fine and from his smoke test, there was plenty coming out of the chimney and I saw it being pulled up the liner quite strongly
He left behind a lovely little certificate to say it's been tested and is functional so I can now crack on and rebuild that infill - well, I can in 3 weeks when I've stopped taxing/working/visiting etc :-(
There will be questions, stand by your keyboard ...